Harry Kane struck for England in injury time after Leigh Griffiths had scored two wonderful free kicks in the final three minutes of normal time.
"It was probably one of the most emotional games ever in my managerial career. As a manager that was hard work. All sorts of emotions," Strachan told reporters.
The former Scotland and Manchester United midfielder said he was impressed with the physical presence of Gareth Southgate's young England side -- and how his men coped with it.
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"I have got to say it was like watching a heavyweight boxer versus a middleweight. These guys are giants and they are playing at a different level to most of us and they kept coming back, with their strength and power and speed it is hard to deal with. They keep coming back at you," he said.
"Whatever you think about this group of players, I tell you one thing, you can’t question their personality, character, commitment. That was beyond the call of duty and there is no-one here who knows how it hard is to play against those players on a day like that," he added.
But Strachan, who was in no mood to criticise his players, admitted there was frustration in the dressing room.
"It is annoying for them –- I can’t be annoyed. It is annoying for them to do so much and have a result that could have been one of the best results ever.
"I’ve also seen Scotland’s best-ever free kick and then I’ve also seen Scotland’s second-best-ever free kick. And then a noise after that, that I have never heard anything like before.
"So these memories will be with me –- I will look at the players and tell them you have to keep coming back and taking knocks like that," he said.
Asked if he really believed the two dead-ball goals were the best ever, Strachan said he could not think of any that were superior strikes.
"I can't, I can't. Of all the years I have been watching Scotland... I remember great goals, I remember Kenny (Dalglish) goals, Charlie Nicholas, but actual strikes?
"And then to do it again. It was probably the tallest wall you could put up in European football today and he went round the side, over the top, he is a good character, a wonderful character, strange but wonderful," he said of the Celtic forward.
(Editing by Clare Fallon)
